Bode envelope bounds for linear time-invariant systems affected by semialgebraic parametric uncertainty

In this paper we address the computation of the Bode plots for linear time-invariant systems affected by semi-algebraic parameteric uncertainty. The problem of computing Bode magnitude and phase bounds is formulated in terms of non-convex semialgebraic optimization and solved by means of semidefinite (SDP) relaxation techniques. Simulation examples are provided to illustrate the effectiveness of the proposed technique.